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Indirect estimation of alpha-stable distributions and processes

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Abstract

The alpha-stable family of distributions constitutes a generalization of the Gaussian distribution, allowing for asymmetry and thicker tails. Its practical usefulness is coupled with a marked theoretical appeal, as it stems from a generalized version of the central limit theorem in which the assumption of the finiteness of the variance is replaced by a less restrictive assumption concerning a somehow regular behavior of the tails. Estimation difficulties have however hindered its diffusion among practitioners. Since simulated values from alpha-stable distributions can be straightforwardly obtained, the indirect inference approach could prove useful to overcome these estimation difficulties. In this paper we provide a description of how to implement such a method by using a skew-t distribution as an auxiliary model. The indirect inference approach will be introduced in the setting of the estimation of the distribution parameters and then extended to linear time series models with alpha-stable disturbances. The performance of this estimation method is then assessed on simulated data. An application on time-series models for the inflation rate concludes the paper.

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Paper provided by Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" in its series Econometrics Working Papers Archive with number wp2004_07.

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Length: 23 pages
Date of creation: 01 Jun 2004
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Handle: RePEc:fir:econom:wp2004_07

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Keywords: Indirect inference; Alpha-stable distributions; Heavy tails.;

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References

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  1. Lombardi, Marco J., 2007. "Bayesian inference for [alpha]-stable distributions: A random walk MCMC approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(5), pages 2688-2700, February.
  2. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  3. Gourieroux, C. & Monfort, A. & Renault, E., 1992. "Indirect Inference," Papers 92.279, Toulouse - GREMAQ.
  4. Giorgio Calzolari & Gabriele Fiorentini & Enrique Sentana, 2004. "Constrained Indirect Estimation," Review of Economic Studies, Wiley Blackwell, vol. 71(4), pages 945-973, October.
  5. repec:cup:etheor:v:12:y:1996:i:4:p:657-81 is not listed on IDEAS
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Cited by:
  1. Greg Hannsgen, 2011. "Infinite-variance, Alpha-stable Shocks in Monetary SVAR: Final Working Paper Version," Economics Working Paper Archive wp_682, Levy Economics Institute, The.
  2. Lombardi, Marco J. & Calzolari, Giorgio, 2009. "Indirect estimation of [alpha]-stable stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2298-2308, April.
  3. Parrini, Alessandro, 2012. "Indirect estimation of GARCH models with alpha-stable innovations," MPRA Paper 38544, University Library of Munich, Germany.

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